SOLUTION: The sum of the square of a positive number and the square of 3 more than the number is 65. What is the number?

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Question 945127: The sum of the square of a positive number and the square of 3 more than the number is 65. What is the number?
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
Let x be the positive number


Subtract 65 from each side
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=484 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4, -7. Here's your graph:

ANSWERS 4,-7 The number is restricted to positive numbers so the answer is 4.
CHECK:



65=65

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